Harmonics, which also are known as “chimes,” are a popular special effect played on certain stringed instruments, for example, banjos, and sometimes guitars, mandolins, and so on. The notes available from common prior art chiming, however, are noticeably limited. On fretted instruments, they are commonly known to be played on open strings by lightly touching the string at the fifth, seventh, twelfth, seventeenth or nineteenth fret position with a finger of the “fretting” hand, and plucking the string with the “picking” hand by a finger or thumb, nail or pick. The finger of the fretting hand may be lifted as the string is plucked to allow the ring of the chime to be sustained longer. That harmonic chime at the twelfth fret rings at an octave above the pitch of its open string and has a node at the twelfth fret location, which is half way between the nut and the bridge, to divide the string into two even segments; at the fifth or seventeenth fret, two octaves above the open string, where nodes are formed from a division of the string into four even segments; and at the seventh or nineteenth fret rings, “so,” an octave higher than the fifth note in the common major scale from the open string, where nodes are formed from a division of the string into three even segments. Thus, if a string were tuned to G, the twelfth fret harmonic chime for that string would be heard as G one octave higher than the open note; the fifth or seventeenth fret harmonic chime would be heard as G two octaves higher than the open note; and the seventh or nineteenth fret harmonic chime would be heard as a D-note higher in pitch than the twelfth fret harmonic but lower in pitch than the fifth or seventeenth fret harmonic. Other harmonics can be found at other positions, one notable example being the fourth or ninth fret positions, for example, which for an open G-string would ring as a high B-note, where nodes are located from division of the string into five segments, although fainter than the aforementioned. Although in theory harmonics can be sounded at other positions, they are usually too faint or high in tone to be effectively played or heard. Harmonics on open strings, i.e., a string that has its full length from the nut of the instrument to its bridge, are termed, “natural harmonics.”
A 5-string banjo is commonly tuned to an open G-tuning (gDGBD). Thus, the harmonics played at the fifth and twelfth frets are from notes of a G-chord (I-chord), and the chimes played at the seventh fret are from notes of a D-chord (V-chord). If a banjo player wished to play harmonics, he thus would generally be limited to playing the notes, G, A, B, D, F# and G. He also could chime a high D# in that G-tuning by playing a chime on the second string, fourth fret position. In back-up or solo work in the standard G-tuning, the banjo player can play chimes effectively while a G-chord or D-chord is playing. These are natural harmonics. However, many if not most songs also employ the IV-chord, which in a song played in the key of G is a C-chord. In common G-tuning on the banjo, many notes from the C-chord are inaccessible through known chiming for that instrument, for example, C-, E- and F-notes.
Guitars in standard tuning are tuned E, A, D, G, B, E, which does not make a major chord (whereas resophonic guitars commonly are tuned to an open G, sometimes an open D, E or E7). With a guitar in standard tuning, natural harmonics at the fifth and seventh fret positions are useful to tune the strings by fifths and octaves, but may not employed as frequently in performance as done with the 5-string banjo.
Mandolins, which have double strings, are commonly tuned in sevenths, like violins, i.e., G, D, A, E, which again does not make a major chord. Natural harmonics can be used to tune the mandolin, but, as with guitars, are not often used in performance.
It is known in certain stringed instruments, at least with such instruments as violins, violas, cellos and double basses, to make not only natural harmonics but also to make in a limited fashion what are termed, “artificial harmonics.” The latter are formed on a point on a string stopped by a finger. These are normally known to be executed, for example, on the violin and viola by solidly stopping the string on the fingerboard with the index finger and lightly touching the node a perfect fourth higher with the little finger. This produces a harmonic pitch two octaves higher than the stopped pitch of the string. Because of their longer string lengths, the cello and double bass typically require the thumb to stop the string and the ring finger to excite the harmonic. The string length on the double bass is so long that the perfect fourth can only be reached in the higher positions of the fingerboard. Different artificial harmonics are known to be produced by thus touching a perfect fifth above the stopped pitch and a major third above the stopped pitch. The major third harmonic is more often employed on the double bass because of its shorter length from the stopped string. Slides between pitches, i.e., glissandos, are known to work well with artificial harmonics, for example, in cello music. There the exciting finger may be moved along the string in relation to the stopped finger to keep the appropriate interval for the desired tone, or not moved to obtain certain effects. The instrument is understood to be bowed during the slide to sustain the glissando sound.